Dynamical systems theory (DST) is a branch of mathematics that assesses abstract or physical systems that change over time. It has a quantitative part (mathematical equations) and a related qualitative part (plotting equations in a state space). Nonlinear dynamical systems theory applies the same tools in research involving phenomena such as chaos and hysteresis. These approaches have provided different ways of investigating and understanding cognitive systems in cognitive science and neuroscience. The ‘dynamical hypothesis’ claims (...) that cognition is and can be understood as dynamical systems. Common consequences for such an approach include rejecting understanding cognition as information processing in nature, including eschewing explanatory roles for computation or representation. Contemporary applications of DST include mouse‐tracking studies in cognitive science and nonrepresentational perspectives on motor control in neuroscience. Such work has philosophical implications concerning the boundaries of cognition, explanation, and representations. DST offers powerful methodology and theories that raise many topics of philosophical significance. (shrink)

It is often claimed (1) that levels of nature are related by supervenience, and (2) that processes occurring at particular levels of nature should be studied using dynamical systems theory. However, there has been little consideration of how these claims are related. To address the issue, I show how supervenience relations give rise to ‘supervenience functions’, and use these functions to show how dynamical systems at different levels are related to one another. I then use this analysis (...) to describe a graded approach to non-reductive physicalism, and to critically assess Davidson’s arguments for psychological anomaly. I also show how this approach can inform empirical research in cognitive science. (shrink)

I examine explanations’ realist commitments in relation to dynamical systems theory. First I rebut an ‘explanatory indispensability argument’ for mathematical realism from the explanatory power of phase spaces (Lyon and Colyvan 2007). Then I critically consider a possible way of strengthening the indispensability argument by reference to attractors in dynamical systems theory. The take-home message is that understanding of the modal character of explanations (in dynamical systems theory) can undermine platonist arguments from explanatory indispensability.

We define a mathematical formalism based on the concept of an ‘‘open dynamical system” and show how it can be used to model embodied cognition. This formalism extends classical dynamical systems theory by distinguishing a ‘‘total system’’ (which models an agent in an environment) and an ‘‘agent system’’ (which models an agent by itself), and it includes tools for analyzing the collections of overlapping paths that occur in an embedded agent's state space. To illustrate the way this formalism (...) can be applied, several neural network models are embedded in a simple model environment. Such phenomena as masking, perceptual ambiguity, and priming are then observed. We also use this formalism to reinterpret examples from the embodiment literature, arguing that it provides for a more thorough analysis of the relevant phenomena. (shrink)

Dynamical systems theory (DST) is gaining popularity in cognitive science and philosophy of mind. Recently several authors (e.g. J.A.S. Kelso, 1995; A. Juarrero, 1999; F. Varela and E. Thompson, 2001) offered a DST approach to mental causation as an alternative for models of mental causation in the line of Jaegwon Kim (e.g. 1998). They claim that some dynamical systems exhibit a form of global to local determination or downward causation in that the large-scale, global activity of the (...) system governs or constrains local interactions. This form of downward causation is the key to the DST model of mental causation. In this paper I evaluate the DST approach to mental causation. I will argue that the main problem for current DST approaches to mental causation is that they lack a clear metaphysics. I propose one metaphysical framework (Gillett, 2002a/b/c) that might deal with this deficiency. (shrink)

Dynamic systems theory is a way of describing the patterns that emerge from relationships in the universe. In the study of interpersonal relationships, within and between species, the scientist is an active and engaged participant in those relationships. Separation between self and other, scientist and subject, runs counter to systems thinking and creates an unnecessary divide between humans and animals.

Neural organization contains a wealth of facts from all areas of brain research and provides a useful overview of physiological data for those working outside the immediate field. Furthermore, it gives a good example that the approach of dynamical system theory together with the concepts of cooperative and competitive interaction can be fruitful for an interdisciplinary approach to cognition.

Here is an accurate and readable translation of a seminal article by Henri Poincaré that is a classic in the study of dynamical systems popularly called chaos theory. In an effort to understand the stability of orbits in the solar system, Poincaré applied a Hamiltonian formulation to the equations of planetary motion and studied these differential equations in the limited case of three bodies to arrive at properties of the equations' solutions, such as orbital resonances and horseshoe orbits. (...) Poincaré wrote for professional mathematicians and astronomers interested in celestial mechanics and differential equations. Contemporary historians of math or science and researchers in dynamical systems and planetary motion with an interest in the origin or history of their field will find his work fascinating. (shrink)

Dynamic systems theory (DS) provides tools for exploring how simpler elements can interact to produce complex psychological configurations. It may, as Lewis demonstrates, provide means for explicating relationships between two reductionist approaches to overlapping sets of phenomena. The result is a description of psychological phenomena at a level that begins to achieve the richness we would hope to achieve in examining psychological life as it is experienced and explored in psychoanalysis.

From his earliest work forward, phenomenologist Maurice Merleau-Ponty attempted to develop a new ontology of nature that would avoid the antinomies of realism and idealism by showing that nature has its own intrinsic sense which is prior to reflection. The key to this new ontology was the concept of form, which he appropriated from Gestalt psychology. However, Merleau-Ponty struggled to give a positive characterization of the phenomenon of form which would clarify its ontological status. Evan Thompson has recently taken up (...) Merleau-Ponty’s ontology as the basis for a new, “enactive” approach to cognitive science, synthesizing it with concepts from dynamic systems theory and Francisco Varela’s theory of autopoiesis. However, Thompson does not quite succeed in resolving the ambiguities in Merleau-Ponty’s account of form. This article builds on an indication from Thompson in order to propose a new account of form as asymmetry, and of the genesis of form in nature as symmetry-breaking. These concepts help us to escape the antinomies of Modern thought by showing how nature is the autoproduction of a sense which can only be known by an embodied perceiver. (shrink)

This article discusses the role of moment-to-moment affect dynamics in mental disorder and aims to integrate recent literature on this topic in the context of complex dynamical system theory. First, we will review the relevance of temporal and contextual aspects of affect dynamics in relation to psychopathology. Related to this, we will discuss recent insights resulting from a network view on affect dynamics in psychopathology. Next, we explore how we can reconcile literature findings from a perspective of complex dynamical (...) system theory. Finally, future directions with regard to personalized assessment of risk and diagnostic use are discussed. (shrink)

On an influential account, chaos is explained in terms of random behaviour; and random behaviour in turn is explained in terms of having positive Kolmogorov-Sinai entropy (KSE). Though intuitively plausible, the association of the KSE with random behaviour needs justification since the definition of the KSE does not make reference to any notion that is connected to randomness. I provide this justification for the case of Hamiltonian systems by proving that the KSE is equivalent to a generalized version of (...) Shannon's communication-theoretic entropy under certain plausible assumptions. I then discuss consequences of this equivalence for randomness in chaotic dynamical systems. Introduction Elements of dynamical systems theory Entropy in communication theory Entropy in dynamical systems theory Comparison with other accounts Product versus process randomness. (shrink)

Dynamical systems are mathematical structures whose aim is to describe the evolution of an arbitrary deterministic system through time, which is typically modeled as (a subset of) the integers or the real numbers. We show that it is possible to generalize the standard notion of a dynamical system, so that its time dimension is only required to possess the algebraic structure of a monoid: first, we endow any dynamical system with an associated graph and, second, we prove that such (...) a graph is a category if and only if the time model of the dynamical system is a monoid. In addition, we show that the general notion of a dynamical system allows us not only to define a family of meaningful dynamical concepts, but also to distinguish among a cluster of otherwise tangled notions of reversibility, whose logical relationships are finally analyzed. (shrink)

A study of shifts in scientific strategies for measuring the living body, especially in dynamic systems theory: sheds light on Hegel's concept of measure in The Science of Logic, and the dialectical transition from categories of being to categories of essence; shows how Hegel's speculative logic anticipates and analyzes key tensions in scientific attempts to measure and conceive the dynamic agency of the body. The study's analysis of the body as having an essentially dynamic identity (...) irreducible to measurement aims to contribute to reconceiving the body, in a way that may be helpful to overcoming dualism. (shrink)

Marr's seminal work laid out a program of research by specifying key questions for cognitive science at different levels of analysis. Because dynamic systems theory focuses on time and interdependence of components, DST research programs come to very different conclusions regarding the nature of cognitive change. We review a specific DST approach to cognitive-level processes: dynamic field theory. We review research applying DFT to several cognitive-level processes: object permanence, naming hierarchical categories, and inferring intent, that (...) demonstrate the difference in understanding of behavior and cognition that results from a DST perspective. These point to a central challenge for cognitive science research as defined by Marr—emergence. We argue that appreciating emergence raises questions about the utility of computational-level analyses and opens the door to insights concerning the origin of novel forms of behavior and thought. We contend this is one of the most fundamental questions about cognition and behavior. (shrink)

The concepts and powerful mathematical tools of Dynamical Systems Theory (DST) yield illuminating methods of studying cognitive processes, and are even claimed by some to enable us to bridge the notorious explanatory gap separating mind and matter. This article includes an analysis of some of the conceptual and empirical progress Dynamical Systems Theory is claimed to accomodate. While sympathetic to the dynamicist program in principle, this article will attempt to formulate a series of problems the proponents (...) of the approach in question will need to face if they wish to prolong their optimism. The main points to be addressed involve the reductive tendencies inherent in Dynamical Systems Theory, its somewhat muddled position relative to connectionism, the metaphorical nature DST-C exhibits which hinders its explanatory potential, and DST-C's problematic account of causality. Brief discussions of the mathematical and philosophical backgrounds of DST, seminal experimental work and possible adaptations of the theory or alternative suggestions (dynamicist connectionism, neurophenomenology, R&D theory) are included. (shrink)

It is now widely accepted that qualitative and quantitative research traditions, rather than being seen as opposed to or in competition with each other should be used, where appropriate, in some kind of combination. How this combining is to be understood ontologically, and therefore epistemologically, however, is not always clear. Rather than endlessly discussing the relationship between different approaches, this paper explores some of the assumptions of the ontologies that underpin such apparent differences, arguing that approaches which declare themselves to (...) be distinct theoretically are often surprisingly similar methodologically. It is argued that dominant ontologies and epistemologies struggle with the conceptualisation and representation of particularity, difference, process, interactions through time, multiple and de-centred forms of causation, and dynamic structure. Complexity/dynamic systems theory is then introduced and examined for its potential to offer the basis of a different kind of ontology: one which is able not only to accommodate these things, but which is itself based upon them. In conclusion, the implications of this perspective are discussed in relation to the problems that have been identified, particularly in relation to the conceptualisation of 'context'. (shrink)

It is now widely accepted that qualitative and quantitative research traditions, rather than being seen as opposed to or in competition with each other ( ; ) should be used, where appropriate, in some kind of combination (; ). How this combining is to be understood ontologically, and therefore epistemologically, however, is not always clear. Rather than endlessly discussing the relationship between different approaches, this paper explores some of the assumptions of the ontologies that underpin such apparent differences, arguing that (...) approaches which declare themselves to be distinct theoretically are often surprisingly similar methodologically. It is argued that dominant ontologies and epistemologies struggle with the conceptualisation and representation of particularity, difference, process, interactions through time, multiple and de‐centred forms of causation, and dynamic structure. Complexity/dynamic systems theory is then introduced and examined for its potential to offer the basis of a different kind of ontology: one which is able not only to accommodate these things, but which is itself based upon them. In conclusion, the implications of this perspective are discussed in relation to the problems that have been identified, particularly in relation to the conceptualisation of ‘context’. (shrink)

It is widely believed that mathematics carries a substantial part of the explanatory burden in science. However, mathematics can also play important heuristic roles of a different kind, being a source of new ideas and approaches, allowing us to build toy models, enhancing expressive power and providing fruitful conceptualizations. In this paper, we focus on the application of dynamical systems theory (DST) within the extended cognition (EC) field of cognitive science, considering this case study to be a good (...) illustration of a general phenomenon. In the paper, we justify both a negative and a positive claim. The negative claim is that dynamical systems theory hardly plays any explanatory role in EC research. We justify our claim by analyzing several accounts of the explanatory role of mathematics and stressing the way mathematical arguments are used in explanations. Our positive claim is that even though, for now, DST has no explanatory power in many of the EC approaches, it still plays an important heuristic role there. In particular, using mathematical notions improves the expressive power of the language and gives a sense of understanding of the phenomena under investigation. The case study of EC allows us to identify and analyze this important role of mathematics, which seems to be neglected in contemporary discussions. (shrink)

Lewis describes the developmental core of dynamic systems theory. I offer recent data from developmental neuroscience on the sequential experience-dependent maturation of components of the limbic system over the stages of infancy. Increasing interconnectivity within the vertically integrated limbic system allows for more complex appraisals of emotional value. The earliest organization of limbic structures has an enduring impact on all later emotional processing.

Griffiths and Russell D. Gray (1994, 1997, 2001) have argued that the fundamental unit of analysis in developmental systems theory should be a process – the life cycle – and not a set of developmental resources and interactions between those resources. The key concepts of developmental systems theory, epigenesis and developmental dynamics, both also suggest a process view of the units of development. This chapter explores in more depth the features of developmental systems theory (...) that favour treating processes as fundamental in biology and examines the continuity between developmental systems theory and ideas about process in the work of several major figures in early 20th century biology, most notable C.H Waddington. (shrink)

This article reports on a study that took a Dynamic Systems Theory perspective to second language motivational self system. More specifically, it investigated the influence of an Intensive English Reading course based on the Production-Oriented Approach upon the L2MSS of Chinese university English majorsfrom the DST perspective. To this end, two intact classes composed of 50 students were assigned into experimental group and control group, who responded to an L2MSS scale before and after the one-semester intervention. Eight (...) and five students were respectively selected using the purposive sampling method from the experimental and control groups for follow-up semi-structured interviews. The quantitative results revealed that the overall and dimensional levels of L2MSS were significantly strengthened over time in the EG while kept stable in the CG. The qualitative results suggested that the enhanced Ideal L2 Self of the participants stemmed from an attractor basin that was deepened by a number of attractors encompassing Output Tasks and Peer Performance. The interview results also showed that the increased L2 Learning Experience of the participants pertained to an attractor basin that was consolidated by an array of attractors containing Output Tasks, Teacher Guidance, Group Discussion, and Peer Assessment. The findings indicated that the attractors at the subjective and social dimensions in the POA-based course collectively worked together to cause changes in L2MSS among the participants. The implications for intervening L2 motivation from a POA approach in English as a Foreign Language classrooms were discussed. (shrink)

Bruineberg and colleagues highlight work using Markov blankets to demarcate the bounds of the mind. This echoes earlier attempts to demarcate the bounds of the mind from a dynamical systems perspective. Advocates of mechanistic explanation have challenged the dynamical approach to independently motivate the application of the formalism, a challenge that Markov blanket theorists must also meet.

This commentary construes the relation between the two systems of temporal updating and temporal reasoning as a bifurcation and tracks it across three time scales: phylogeny, ontogeny, and microgeny. In taking a dynamic systems approach, flexibility, as mentioned by Hoerl & McCormack, is revealed as the key characteristic of human temporal cognition.

Although we applaud the interactivist approach to language and communication taken in the target article, we notice that Shanker & King (S&K) give little attention to the theoretical frameworks developed by dynamical system theorists. We point out how the dynamical idea of causality, viewed as multidirectional across multiple scales of organization, could further strengthen the position taken in the target article.

Economic logic impinges on contemporary political theory through both economic reductionism and economic methodology applied to political decision-making (through game theory). The authors argue that the sort of models used are based on mechanistic and linear methodologies that have now been found wanting in physics. They further argue that complexity based self-organization methods are better suited to model the complexities of economy and polity and their interactions with the overall social system.

Years ago, when I was an undergraduate math major at the University of Wyoming, I came across an interesting book in our library. It was a book of counterexamples t o propositions in real analysis (the mathematics of the real numbers). Mathematicians work more or less like the rest of us. They consider propositions. If one seems to them to be plausibly true, then they set about to prove it, to establish the proposition as a theorem. Instead o f setting (...) out to prove propositions, the psychologists, neuroscientists, and other empirical types among us, set out to show that a proposition is supported by the data, and that it is the best such proposition so supported. The philosophers among us, when they are not causing trouble by arguing that AI is a dead end or that cognitive science can get along without representations, work pretty much like the mathematicians: we set out to prove certain propositions true on the basis of logic, first principles, plausible assumptions, and others' data. But, back to the book of real analysis counterexamples. If some mathematician happened t o think that some proposition about continuity, say, was plausibly true, he or she would then set out to prove it. If the proposition was in fact not a theorem, then a lot of precious time would be wasted trying to prove it. Wouldn't it be great to have a book that listed plausibly true propositions that were in fact not true, and listed with each such proposition a counterexample to it? Of course it would. (shrink)

This chapter contains sections titled: How is the Combining of Qualitative/Quantitative Methods to be Understood? ‘Critical Connections’? Problems Conceptualising and Researching Difference, Specificity and Context Complexity Theory: Redefining Order (and Chaos)? A Complexity‐Based Ontology Conceptualising Difference, Specificity and Context Conclusion Notes References.

I propose a semi-eliminative reduction of Fodors concept of module to the concept of attractor basin which is used in Cognitive Dynamic Systems Theory (DST). I show how attractor basins perform the same explanatory function as modules in several DST based research program. Attractor basins in some organic dynamic systems have even been able to perform cognitive functions which are equivalent to the If/Then/Else loop in the computer language LISP. I suggest directions for future research (...) programs which could find similar equivalencies between organic dynamic systems and other cognitive functions. This type of research could help us discover how (and/or if) it is possible to use Dynamic Systems Theory to more accurately model the cognitive functions that are now being modeled by subroutines in Symbolic AI computer models. If such a reduction of subroutines to basins of attraction is possible, it could free AI from the limitations that prompted Fodor to say that it was impossible to model certain higher level cognitive functions. (shrink)

From birth to 15 months infants and caregivers form a fundamentally intersubjective, dyadic unit within which the infant’s ability to recognize gender/sex in the world develops. Between about 18 and 36 months the infant accumulates an increasingly clear and subjective sense of self as female or male. We know little about how the precursors to gender/sex identity form during the intersubjective period, nor how they transform into an independent sense of self by 3 years of age. In this Theory (...) and Hypothesis article I offer a general framework for thinking about this problem. I propose that through repetition and patterning, the dyadic interactions in which infants and caregivers engage imbue the infant with an embodied, i.e., sensori-motor understanding of gender/sex. During this developmental period (which I label Phase 1) gender/sex is primarily an intersubjective project. From 15 to 18 months (which I label Phase 2) there are few reports of newly appearing gender/sex behavioral differences, and I hypothesize that this absence reflects a period of developmental instability during which there is a transition from gender/sex as primarily inter-subjective to gender/sex as primarily subjective. Beginning at 18 months (i.e., the start of Phase 3), a toddler’s subjective sense of self as having a gender/sex emerges, and it solidifies by 3 years of age. I propose a dynamic systems perspective to track how infants first assimilate gender/sex information during the intersubjective period (birth to 15 months); then explore what changes might occur during a hypothesized phase transition (15 to 18 months), and finally, review the emergence and initial stabilization of individual subjectivity-the period from 18 to 36 months. The critical questions explored focus on how to model and translate data from very different experimental disciplines, especially neuroscience, physiology, developmental psychology and cognitive development. I close by proposing the formation of a research consortium on gender/sex development during the first 3 years after birth. (shrink)

Bridging between psychological and neurobiological systems requires that the system components are closely specified at both the psychological and brain levels of analysis. We argue that in developing his dynamic systems theory framework, Lewis has sidestepped the notion of a psychological level systems model altogether, and has taken a partisan approach to his exposition of a brain-level systems model.

Efforts to bridge emotion theory with neurobiology can be facilitated by dynamic systems (DS) modeling. DS principles stipulate higher-order wholes emerging from lower-order constituents through bidirectional causal processes cognition relations. I then present a psychological model based on this reconceptualization, identifying trigger, self-amplification, and self-stabilization phases of emotion-appraisal states, leading to consolidating traits. The article goes on to describe neural structures and functions involved in appraisal and emotion, as well as DS mechanisms of integration by which they (...) interact. These mechanisms include nested feedback interactions, global effects of neuromodulation, vertical integration, action-monitoring, and synaptic plasticity, and they are modeled in terms of both functional integration and temporal synchronization. I end by elaborating the psychological model of emotion–appraisal states with reference to neural processes. (shrink)

Lewis's dynamical systems emotion theory continues a tradition including Merleau-Ponty, von Bertallanfy, and Aristotle. Understandably for a young theory, Lewis's new predictions do not follow strictly from the theory; thus their failure would not disconfirm the theory, nor their success confirm it – especially given that other self-organizational approaches to emotion (e.g., those of Ellis and of Newton) may not be inconsistent with these same predictions.

The problem of the direction of time is reconsidered in the light of a generalized version of the theory of abstract deterministic dynamical systems, thanks to which the mathematical model of time can be provided with an internal dynamics, solely depending on its algebraic structure. This result calls for a reinterpretation of the directional properties of physical time, which have been typically understood in a strictly topological sense, as well as for a reexamination of the theoretical meaning of (...) the widespread time-reversal invariance of classical physical processes. (shrink)

This work addresses a broad range of questions which belong to four fields: computation theory, general philosophy of science, philosophy of cognitive science, and philosophy of mind. Dynamical system theory provides the framework for a unified treatment of these questions. ;The main goal of this dissertation is to propose a new view of the aims and methods of cognitive science--the dynamical approach . According to this view, the object of cognitive science is a particular set of dynamical (...) class='Hi'>systems, which I call "cognitive systems". The goal of a cognitive study is to specify a dynamical model of a cognitive system, and then use this model to produce a detailed account of the specific cognitive abilities of that system. The dynamical approach does not limit a-priori the form of the dynamical models which cognitive science may consider. In particular, this approach is compatible with both computational and connectionist modeling, for both computational systems and connectionist networks are special types of dynamical systems. ;To substantiate these methodological claims about cognitive science, I deal first with two questions in two different fields: What is a computational system? What is a dynamical explanation of a deterministic process? ;Intuitively, a computational system is a deterministic system which evolves in discrete time steps, and which can be described in an effective way. In chapter 1, I give a formal definition of this concept which employs the notions of isomorphism between dynamical systems, and of Turing computable function. In chapter 2, I propose a more comprehensive analysis which is based on a natural generalization of the concept of Turing machine. ;The goal of chapter 3 is to develop a theory of the dynamical explanation of a deterministic process. By a "dynamical explanation" I mean the specification of a dynamical model of the system or process which we want to explain. I start from the analysis of a specific type of explanandum--dynamical phenomena--and I then use this analysis to shed light on the general form of a dynamical explanation. Finally, I analyze the structure of those theories which generate explanations of this form, namely dynamical theories. (shrink)